#pilot waves

20ish years ago, a team of physicists observed that droplets of oil bouncing on vibrating water behaved in ways reminiscent of quantum systems. Because the vibrations sort of quantized the water surface, the bounces of the droplets followed quantized steps. Furthermore, the droplets themselves caused displacement of the water, changing the water waves. It all looked sort of like quantized electron orbitals in an atom. And then, of course, if the scientists put in barriers, the droplets could sometimes happen to bounce over them--tunneling. And most astonishing of all, if they placed barriers in a double slit pattern, the wave nature of the water waves guided the droplets into a diffraction-like pattern. That is, the particles behaved like waves because they were simultaneously guided by and inducing waves.

So of course, several groups jumped to try to replicate it. And after about a dozen years they came back with: it didn't work. They didn't see any double-slit diffraction patterns--the droplets interacting with the water waves were not themselves acting like waves. The original experiment had only run 75 times, and had a noisy system; a small sample size plus noise and it was easy to see interference "stripes" that weren't really there. Larger, more careful experiments did not reproduce the results.

There's actually a theoretical reason why classical pilot waves can't reproduce the quantum double-slit experiment. The quantum double-slit experiment is symmetric: the wavefunction passes equally through both slits, and the resulting interference pattern reflects that. That's also true of classical waves passing through a double slit (we did this demo in high school with a tub of water and some bricks). But as soon as you add the oil droplet, the droplet does go through one side or the other, and because its interaction with the waves affects the waves as well as the waves affecting the droplet, that means it breaks the symmetry of the waves themselves. The resulting diffraction pattern is different depending on which side of the double slit the oil droplet goes through.

(Quantum pilot waves don't work quite the same way, so this argument doesn't pertain to them. They're still a viable quantum interpretation.)

Pilot-wave theories, the best-known and -studied of which is the de Broglie-Bohm theory, are physical theories intended to provide a realist microphysics that yields the same statistical predictions as standard quantum theory. Misconceptions and outright false claims about pilot-wave theories abound, so I’ve paired some of these claims with references to debunk them here.

Supposedly, pilot-wave theories

are ruled out by Bell’s theorem [0] (particularly ironic as Bell was a vocal proponent of such theories and came up with his theorem to defend them)

can’t be extended to treat relativistic (spinning or otherwise) particles [1]

can’t be extended to (relativistic or otherwise) field theories [2, 3, 4]

can’t make novel, testable predictions that differ from standard quantum theory [5]

are necessarily “one-world” rather than “many-worlds” theories [6]

describe quantum systems in terms of trajectories that are fundamentally unobservable [7]

don’t help us calculate anything we can’t just as easily get from standard quantum theory [8, section 4.2]

yield no insight into the Born rule  [9, 10, 11]

So, first of all, if you assume quantum mechanics is true--and empirically it is--you can’t really explain how it produces experimental outcomes. It kinda just does. People understandably don’t really like that--although you get used to it over time if you have to deal with it a lot. And eventually you just accept it and become complacent and stop thinking... which I really don’t want to be that person, so even though I’m just an experimentalist I try to revisit this topic from time to time.

So anyway, there was this guy, John Stewart Bell, who in the 1950s (60s?) mathematically proved that if quantum mechanics were regular-old deterministic, that is if action A necessarily led to result B (which is how you instinctively expect the world to work), you’d get a certain set of results to a certain set of simple experiments. And if you don’t get those results--and experiments have shown that you definitely don’t--then the world is not simply deterministic. But that does leave you a few options:

non-determinism

this is the most popular and this is the one taught in school to physics majors

instead of determinism you have probabilities

like action A can lead to result B with a 25% probability OR result C with a 75% probability

this is not like chaos where the results seem unpredictable because a tiny change can have a big effect, but if you knew all the tiny stuff and you had a big enough computer you could, in principle, calculate through and figure out the result

no, the results really are very literally unpredictable

some examples of non-deterministic interpretations of quantum mechanics are:

Copenhagenism aka “it’s just probabilities, now shut up and calculate”

so unsatisifying

Many Worlds aka “the universe branches and now there’s a universe where B happened and a universe where C happened”

sci-fi nerds love it

but it’s so overcomplicated while somehow failing to add any usable theories beyond what Copenhagenism already provides

Collapse theory aka “it was literally BOTH B and C until it interacted with something and collapsed into one or the other”

wtf does “collapse” even mean in this context? NO ONE KNOWS

“collapse” being completely undefined and not based on anything except “we need to say something happens” is by far the biggest objection to this one--even bigger than the whole “non-determinism” thing

God rolls dice aka “motherfucking miracles”

honestly this one is exactly the same as Copenhagenism

Eintstein was trying to throw shade at Bohr but he missed

plus lots of other more obscure ones--iirc most quantum interpretations fall in the “non-deterministic” category

generally I personally usually think in terms of collapse theory, especially since that’s the one [second-] most consistent with wave/particle duality, and it’s the one that feels like what’s happening when you do experiments

in school you’re typically taught to believe in some hybrid of Copenhagenism and collapse theory so I guess I’m being uncreative

thus far none of the non-deterministic interpretations have different math behind them or make any predictions that differ from each other so debatably they’re all the same interpretation and if one is true they’re all equally true

I like this because it’s more or less applying collapse theory to philosophy

also fuck many-worlds-ism

non-locality

a local theory says that event A can only affect object B if light has had enough time to travel from A to B

otherwise they’re too far apart and it’s too soon

so non-locality says event A can affect object B instantaneously no matter how far away B is

i.e. faster-than-light communication

the problem is “instantaneous” is not a very coherent topic once you bring relativity into it

it breaks causality: if A affected B before light from A reached B then that means that if you’re moving in the right way and watching this all unfold, B was affected before event A even happened

retro-causality: the future affects the past

an example of a non-local interpretation is Bohmian pilot waves

it’s classically deterministic except that it has retro-causality

personally I think pilot waves may be the theoretically prettiest quantum interpretation so far

but some people find retro-causality inherently ugly

the math is supposed to be pretty hard, though--much harder than regular quantum mechanics

apparently it’s also useful???

(in quantum fluid dynamics, where the math is ugly no matter what, pilot waves are apparently actually less ugly than traditional quantum mechanics)

it’s certainly the only interpretation that has that distinction

well ok, Copehagenism gets people to shut up and calculate and there’s a time and a place for that

since it starts with a different assumption than non-determinism it MAY be possible, sometime in the future, to distinguish between the two and prove only one of them can be true

but if so we haven’t figured out how yet--not even in theory, let alone in practice

non-temporality

this is like non-locality except instead of distance not mattering, time doesn’t matter

people hate this one and don’t talk about it much

the thing is, our monkey-brains (being unable to notice things moving really fast) are primed to assume that distance doesn’t matter but that time does

so non-temporality is a lot more instinctively uncomfortable for humans than non-locality

even though they’re very similar mathematically

superdeterminism

you think event A led to result B? think again

what really happened was event A and object B and your detector all colluded to give you result B

how? how did your detector even know what was going on with event A when it should have only affected object B?

because this collusion has been happening since the Big Bang

the entire universe is in on it; the whole universe from the beginning of time exists only to fuck with your experimental results

and there’s nothing you can do about it because your detector is in on it

and not only that, your brain and hands giving instructions to the detector and building it in the first place, those are all also in on the collusion

there’s no escaping it, result B was ALWAYS inevitable

this one actually is a chaos-based theory but not in a simple way

because Bell’s theorem says even a normal chaos theory is insufficient, because a normal chaos theory is still regular old deterministic

there’s still got to be some deeper thing that we don’t yet understand that causes this collusion to happen beyond a simple--or even complex--chain events (because otherwise it would just be a normal chaos theory)

it’s got to be something about everything being rigged as one unified whole when the universe first formed

event A and result B and your equipment and your mind are all one with the universe and that’s why your experiment turned out the way it did

I’ve seen it argued that non-temporality, rather than being different but similar to non-locality, is actually better thought of as a type of superdeterminism, which is something I can only just wrap my head around on a good day but I think I agree that that’s the only way non-temporality can actually get you any consistent results to your experiment whatsoever

The most standard objection to superdeterminism is that it doesn’t allow for free will. That’s a pretty absurd objection, because regular determinism, which we all take for granted as being true when we’re talking about physics (even though it’s not true in the context of quantum mechanics) also voids free will. And so does probabilistic non-determinism; being ruled by probabilities (or branching universes or whatever) doesn’t give you an active choice, either. And non-locality and non-temporality with their respective versions of retro-causality don’t easily allow for free will either, especially since the whole point of trying to use them is they can let you be just regular-old deterministic (as long as you’re ok with the future affecting the past). When you’re talking about physics, free will is just a non-starter. If you want free will you have to talk about emergent systems, which may be within the scope of physics but is definitely beyond the scope of quantum interpretation.

The most standard objection to non-determinism, on the other hand, is it’s too nihilistic. “Shut up and calculate”? What kind of a message is that even sending to our children?

The thing about superdeterminism, though, is for it to work you need some deep-level correlations between everything in the universe. The problem with that, as I understand it--and note that from here on out this is my personal synthesis, so at this point in the post we’re veering away from established philosophy-of-physics--is that correlation is extremely delicate. Look at some classical correlation, like gravity pulling stuff together so a bunch of stuff accumulates in about the same place: all that stuff’s positions are correlated. As soon as you have an outside object, not part of the correlated system, strongly interacting with it, the correlation is ruined. For example, if the earth gets hit by a huge asteroid (strong interaction) a large chunk of it might un-correlate--as it were--and form the moon, way away up there. Or look at a quantum correlation like entanglement (and entanglement is one of the main phenomena that quantum interpretation seeks to address in the first place). Particles A and B are correlated: they’re either both in state C or they’re both in state D; you can’t have one being C while the other is being D. The moment you have a strong interaction, though, like a collision with a photon, or your detector doing its detecting to see whether they’re in state C or D, or they hit an air molecule, or whatever, the moment that happens the correlation is gone. It’s all so delicate.

But superdeterminism, like I said, is thought to involve some deeper-level (beyond classical or even quantum) correlation between everything in the universe. And the only way that can work is if everything in the universe is, in a sense, one unified thing. The universe is all that exists; everything within it--everything that exists and everything that happens--is just a representation of the singular universe’s internal state, not actual objects or events with any intrinsic properties or patterns of their own. It renders ourselves, and everything we could ever observe or participate in or understand, as being even less than mere cogs in a machine. And furthermore--delicate as correlations are--there can’t be more universes external to this one, or if there are they’re certainly not interacting with it, because otherwise the correlations would break, and then who knows what would happen (maybe we’d stop getting nonsensical results to quantum experiments).

NASA’s EMDrive And The Quantum Theory Of Pilot Waves

  There has been a lot of digital ink spilled over the recent paper on the reactionless thrust device known as the EMDrive. While it’s clear that a working EM Drive would violate well established scientific theories, what isn’t clear is how such a violation might be resolved. Some have argued that the thrust could be an effect of Unruh radiation, but the authors of the new paper argue instead for…

A beautiful video of pilot wave experiments, which are basically oil droplets bouncing along a liquid surface.  Interestingly, they display properties only before seen in quantum mechanics.